For weakly interacting massive particles (WIMPs) with masses at the TeV scale, there are nonperturbative “Sommerfeld enhancements” to pair annihilation rates due to unsuppressed exchanges of weak gauge bosons before the annihilation. These enhancements are conventionally computed numerically through the solution of coupled-channel Schrödinger equations. The most dramatic enhancements occur when there is an S-wave resonance near the WIMP-pair threshold. My collaborators and I have developed an effective field theory for wino dark matter near such a resonance. Winos interact nonperturbatively through zero-range contact interactions as well as through the long-range Coulomb interaction. Our analytic results for wino scattering and wino-pair annihilation accurately reproduce the results calculated numerically using the Schrödinger equation. In addition, processes involving dark-matter bound states can also be treated analytically using the effective field theory.
